In the right triangle shown, $BC = 4$ and $AB = 10$. What is $AC$ ? $A$ $C$ $B$ $?$ $4$ $10$
Solution: We know $a^2 + b^2 = c^2$ We want to find $b$ ; let $a = 4$ and $c = 10$ So $b^2 = c^2 - a^2 = 10^2 - 4^2 = 84$ Then, $b = \sqrt{84}$ Simplifying the radical gives $b = 2\sqrt{21}.$